Erosion of concrete floor at vinyl tile seams.

I had a water problem with a vinyl tiled basement floor that seems to have eroded the concrete at the edges of some of the tiles up to about 1/8" deep. There was also a lot of efflorescence forming where the erosion was taking place. The water problem is solved and no longer an issue and I want to restore this area.
I'm thinking of filling in the eroded areas and re-tile with vinyl or painting over and adding a few area rugs.
My two questions are:
1. what material is best for filling and smoothing in the eroded areas that would be suitable for vinyl tile installation or painting?
2. there is still vinyl adhesive left on the cement floor that that seems to be well bonded to the concrete floor. If I decide to paint the floor, can I just paint directly over the adhesive or do I need to use a primer first? If so, what paint/primer do you recommend?